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A188494 Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 2.

%I A188494 #34 Dec 27 2015 09:13:26
%S A188494 0,1,2,4,12,42,138,414,1235,3764,11604,35664,109132,333652,1021220,
%T A188494 3127709,9578526,29326904,89785684,274896606,841682902,2577075290,
%U A188494 7890425175,24158602552,73968049928,226473538032,693411153800,2123068036904,6500352097064
%N A188494 Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(1) <= 2.
%C A188494 a(n) is also the permanent of the n X n matrix that has ones on its diagonal, ones on its three superdiagonals, ones on its three subdiagonals (with the exception of zeros in the (3,1) and (4,1)-entries), and is zero elsewhere.
%C A188494 This is row 8 of Kløve's Table 3.
%H A188494 Harvey P. Dale, <a href="/A188494/b188494.txt">Table of n, a(n) for n = 0..1000</a>(first 93 terms from Nathaniel Johnston)
%H A188494 Torleiv Kløve, <a href="http://www.ii.uib.no/publikasjoner/texrap/pdf/2008-376.pdf"> Spheres of Permutations under the Infinity Norm - Permutations with limited displacement</a>, Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
%H A188494 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1).
%F A188494 From _Nathaniel Johnston_, Apr 10 2011: (Start)
%F A188494 a(n) = A188491(n+1) - A002528(n) - A002526(n).
%F A188494 a(n) = A002526(n-1) + A002527(n-1).
%F A188494 (End)
%F A188494 G.f.: x*(x^6 +x^5 -x^4 -x^3 -x^2 +x +1) / (x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2 -x +1). - _Colin Barker_, Dec 13 2014
%p A188494 with(LinearAlgebra):
%p A188494 A188494:= n-> `if`(n=0, 0, Permanent(Matrix(n, (i, j)->
%p A188494               `if`(abs(j-i)<4 and [i, j]<>[3, 1] and [i, j]<>[4, 1], 1, 0)))):
%p A188494 seq(A188494(n), n=0..20);
%t A188494 LinearRecurrence[{1,3,3,13,21,19,3,-7,-9,-5,-3,-3,-1},{0,1,2,4,12,42,138,414,1235,3764,11604,35664,109132},30] (* _Harvey P. Dale_, Dec 27 2015 *)
%o A188494 (PARI) concat(0, Vec(x*(x^6 +x^5 -x^4 -x^3 -x^2 +x +1) / (x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2 -x +1) + O(x^100))) \\ _Colin Barker_, Dec 13 2014
%K A188494 nonn,easy
%O A188494 0,3
%A A188494 _N. J. A. Sloane_, Apr 01 2011
%E A188494 Name and comments edited, and a(12)-a(28) from _Nathaniel Johnston_, Apr 10 2011